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MATHEMATICA BOHEMICA, Vol. 130, No. 4, pp. 355-370 (2005)
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Diameter-invariant graphs

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Ondrej Vacek

* Ondrej Vacek*, Department of Mathematics and Descriptive Geometry, Faculty of Wood Sciences and Technology, Technical University Zvolen, T. G. Masaryka 24, 960 53 Zvolen, Slovak Republic, e-mail: ` o.vacek@vsld.tuzvo.sk`

**Abstract:** The diameter of a graph $G$ is the maximal distance between two vertices of $G$. A graph $G$ is said to be diameter-edge-invariant, if $d(G-e)=d(G)$ for all its edges, diameter-vertex-invariant, if $d(G-v)=d(G)$ for all its vertices and diameter-adding-invariant if $d(G+e)=d(e)$ for all edges of the complement of the edge set of $G$. This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.

**Keywords:** extremal graphs, diameter of graph

**Classification (MSC2000):** 05C12, 05C35

**Full text of the article:**

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